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3 years ago

When Sarah invests $4000 in a money market

Mathematics

1 answer:

gogolik [260]3 years ago

7 0

Answer:

$4,224

Step-by-step explanation:

P(principal)=$4,000

R(rate)=1.4%

T(Time): 4 years

A=4,000×(1+(0.014×4))=$4,224

A=$4,224.00

So, Sarah will have $4,224 of interest in 4 years.

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F(x) = x2 + 9, g(x) = *square root of* x + 8, <br><br> find g(f(x))

ICE Princess25 [194]

Answer:

g(f(x)) = √(x^2 +17)

Step-by-step explanation:

For ...

f(x) = x^2 +9

g(x) = √(x +8)

The definition of g(f(x)) is ...

g(f(x)) = g(x^2 +9) = √((x^2 +9) +8)

g(f(x)) = √(x^2 +17)

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3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago

Simplify each expression(OOF PLEASE HURRY FGHJHGFGHJ):

Svetach [21]

(1) -(5y - 2)= -5y+2

(2) -5 (3n + 1)= -15n - 5

(3) too long to do

6 0

3 years ago

I need help with this！And also can they play 6 levels during their free trial?

djverab [1.8K]

Answer: B and they can play 6 levels

Step-by-step explanation: first solve the mixed fractions

Then solve the factions

7 0

3 years ago

What is the value of the expression (2)^6?<br>pls help

Ronch [10]

Answer:

Step-by-step explanation:

2^6, or 2⁶, is two to the power of six.

Basically you multiply the bottom number (in this case 2) by itself as many times as the the number in the top right (in this case six)

2^6=2*2*2*2*2*2=64

8 0

3 years ago

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